Compressed sensing ocean bottom cable system

Abstract

Embodiments included herein are directed to marine seismic streamers. A marine seismic streamer can include an outer skin formed into a longitudinally extending tubular shape, an inner surface of the outer skin defining an interior volume containing a gel substance. The seismic streamer can also include a plurality of hydrophones and a plurality of microelectromechanical system ("MEMS") sensors associated with the outer skin, wherein the plurality of MEMS sensors are non-uniformly spaced in the seismic streamer along an axial direction of the streamer such that, in the seismic streamer, no more than 100 MEMS sensors are positioned over a continuous 100 meter axial length of the seismic streamer. The seismic streamer can further include an electronics system extending axially through an interior portion of the outer skin and a reinforcing member core extending axially through the interior portion of the outer skin.

Description

[0001] This application is a divisional application of the invention patent application filed on October 4, 2018, with application number 201880071971.1 and invention title "Compression Sensing Marine Towed Cable System".

[0002] Cross-references to related applications

[0003] This application claims the benefit of U.S. Provisional Application No. 62 / 568,141, filed October 4, 2017, and U.S. Provisional Application No. 62 / 570,026, filed October 9, 2017, the entire contents of which are incorporated herein by reference. Background Technology

[0004] This section provides background information to facilitate a better understanding of the various aspects of this disclosure. It should be understood that the statements in this section of this document should be read in this context, rather than as an admission of prior art. Seismic surveys are used to determine various characteristics of strata, such as the presence or absence of various minerals. Seismic surveys can be used to determine the presence of hydrocarbon deposits in strata. Seismic surveys can be conducted by generating pulses using a seismic source, which travel into the strata and thus echo and / or reflect from them. The echoes and / or reflections are then detected and recorded by seismic sensors and recording systems. The resulting data can be analyzed and used to determine the characteristics of the strata. It can be displayed visually or stored as digital data.

[0005] One type of seismic survey is conducted on land and is called land seismic survey. In land seismic survey, pulses are introduced into the strata, and seismic sensors are placed in contact with the strata (on and / or within the strata). Sensors can be hydrophones, seismographs, or other conventional types of sensors capable of detecting the echo and / or reflection of the pulse. A large number of dispersed, interconnected sensors can be used, which are in turn connected to recording devices(s). Some problems encountered in land seismic surveys include lightning strikes, animal damage (e.g., rats chewing cables), and other degradation caused by these elements. Dispersed sensors can be connected via wireless communication, wired communication, or a combination thereof. Sensors can also be in a so-called “blind” configuration, where sensors or groups of sensors are connected to recording devices independent of a central recording unit and are cleared at various times and in various ways.

[0006] Another type of survey is marine seismic survey, which includes towed marine seismic survey. In towed marine seismic survey, a ship tows a series of seismic towlines. Seismic towlines are cables on which and / or integrated seismic sensors are mounted. Similar to terrestrial surveys, marine seismic surveys introduce pulses into the formation. These pulses can be generated by an air gun or a marine vibrator. Multiple pulses can travel through the water and into the formation, where they echo and / or reflect. The echoes and / or reflections return through the water and are detected by the seismic sensors on the towlines and can be recorded. The resulting data can be analyzed and used to determine the characteristics of the formation. It can be displayed visually or stored as data. Seismic sensors located on the seabed can also be used.

[0007] While potentially relevant in all seismic exploration, acquiring multi-component seismic data is valuable because it facilitates numerous data processing aspects, such as deghosting, noise reduction, and other attenuation and processing techniques. In other words, the cost of the equipment is related to its commercial applicability. Multi-component data can be viewed as directional particle motion data, pressure data, rotational data, or combinations thereof in multiple directions. Summary of the Invention

[0008] In one embodiment, a marine seismic towed cable is provided. The marine seismic towed cable may include an outer skin formed in a longitudinally extending tubular shape, the inner surface of which defines an internal volume containing a gel material. The seismic towed cable may also include a plurality of hydrophones and a plurality of microelectromechanical systems (“MEMS”) sensors associated with the outer skin, wherein the plurality of MEMS sensors are non-uniformly spaced along the axial direction of the seismic towed cable, such that no more than 100 MEMS sensors are positioned along a continuous axial length of 100 meters of the seismic towed cable. The marine seismic towed cable may further include an electronic core extending axially through the internal portion of the outer skin, wherein the plurality of MEMS sensors are electrically communicated with the electronic core. The marine seismic towed cable may also include a reinforcing core extending axially through the internal portion of the outer skin.

[0009] In some embodiments, at least two of the plurality of MEMS sensors may be placed adjacent to each other at a spacing of 0.39 meters or less. In another embodiment, the plurality of MEMS sensors may be placed adjacent to each other at a spacing of 0.5 meters or less. The plurality of MEMS sensors may include no more than 80 MEMS sensors over a continuous 100-meter length of the seismic towed cable. The plurality of MEMS sensors may be spaced apart over a continuous 100-meter length of the seismic towed cable at an average spacing greater than the spatial Nyquist interval. One or more adjacent MEMS sensors among the plurality of MEMS sensors may include an average spacing between them of 1 and 4 meters. The average spacing may be greater than approximately 1.78 meters. The sensors may be irregularly spaced relative to each other in the axial direction. The marine seismic towed cable may further include a first sensor attached to a first side of the outer skin and a second sensor attached to a second side of the outer skin. The plurality of sensors may include a three-component (“3C”) MEMS sensor. The marine seismic towed cable may further include one or more seismic towed cable orientation detection devices configured to determine the relative position of at least a portion of the seismic towed cable.

[0010] In another embodiment, a method for performing seismic surveys is provided. The method may include towing a marine seismic towed cable having an outer skin formed in a longitudinally extending tubular shape, the inner surface of which defines an internal volume containing a gel material. The method may further include acquiring seismic data using a plurality of hydrophones and sensors associated with the outer skin, wherein, in the seismic towed cable, for every consecutive 100-meter length of the towed cable, the plurality of sensors include a predetermined maximum number of sensors, wherein the plurality of sensors are axially non-uniformly spaced from each other along the towed cable at an average spacing greater than the spatial Nyquist interval over a consecutive 100-meter length of the seismic towed cable. The method may further include transmitting the seismic data to an electronic system extending axially through the interior of the outer skin, wherein the plurality of sensors are electrically communicated with the electronic system.

[0011] In some implementations, the predetermined number of sensors may not exceed 80. At least two of the plurality of MEMS sensors may be placed adjacent to each other in the axial direction along the tow cable and have a spacing of 0.39 meters or less between them. The plurality of sensors may include three-component (“3C”) sensors.

[0012] In one embodiment, a marine seismic towed cable is provided. The marine seismic towed cable may include an outer skin formed in a longitudinally extending tubular shape, the inner surface of which defines an internal volume containing a gel material. The seismic towed cable may also include a plurality of hydrophones and a plurality of particle motion sensors associated with the outer skin, wherein the plurality of particle motion sensors are non-uniformly spaced along the axial direction of the seismic towed cable, such that no more than 100 particle motion sensors are positioned along a continuous axial length of 100 meters of the seismic towed cable. The particle motion sensors may be non-uniformly distributed along the continuous 100-meter axial length of the seismic towed cable in a repeating pattern at intervals greater than 12.5 meters. The marine seismic towed cable may further include an electronic core extending axially through the interior of the outer skin, wherein the plurality of particle motion sensors are electrically communicated with the electronic core. The marine seismic towed cable may also include a reinforcing core extending axially through the interior of the outer skin.

[0013] In some implementations, particle motion sensors can be non-uniformly distributed along a continuous 100-meter axial length of the seismic tow cable in a repeating pattern at distances greater than 50 meters.

[0014] This overview is provided to introduce some concepts, which will be further described in the detailed description below. This overview is not intended to identify key or essential features of the claimed subject matter, nor is it intended to help limit the scope of the claimed subject matter. Attached Figure Description

[0015] Embodiments of this disclosure are described with reference to the following figures.

[0016] Figure 1A This is a general illustration of a seismic survey vessel with an array of towed seismic cables according to a first embodiment of the present disclosure.

[0017] Figure 1B This is a schematic cross-sectional view showing a portion of a tow cable employing an embodiment of the present disclosure;

[0018] Figure 2 An overall block diagram of the adaptive beamformer according to the present invention is shown;

[0019] Figure 3 This is a schematic diagram of a marine seismic survey system combining multi-component seismic cables and features, based on aspects of this disclosure.

[0020] Figure 4 A portion of the seismic tow cable for decoupling a floating seismic sensor unit is shown in accordance with one or more aspects of this disclosure;

[0021] Figure 5A non-limiting example of a seismic sensor unit equipped with a sensor spacer device according to one or more aspects of this disclosure is shown;

[0022] Figure 6 This is an end view along the longitudinal axis of a seismic sensor unit, which is provided and coupled to a sensor spacer device, according to one or more aspects of this disclosure.

[0023] Figure 7 This is an end view along the longitudinal axis of a seismic cable having an internal seismic sensor unit disposed and coupled to a sensor spacer device and a cable reinforcement member, according to one or more aspects of this disclosure.

[0024] Figure 8 This is an end view along the longitudinal axis of a seismic cable having an internal seismic sensor unit provided with and decoupled from a sensor spacer device and a cable reinforcement member, according to one or more aspects of this disclosure.

[0025] Figure 9 A portion of a seismic tow cable incorporating a seismic sensor unit according to one or more aspects of this disclosure is shown, the seismic sensor unit being provided with a sensor spacer device;

[0026] Figure 10 Two figures are shown to illustrate the noise propagation characteristics of a towed cable platform affected by gel rheology;

[0027] Figure 11 An exemplary tow cable segment according to one or more aspects of this disclosure is shown, including a sensor;

[0028] Figure 12 An exemplary tow cable segment according to one or more aspects of this disclosure is shown, including a sensor;

[0029] Figure 13 An example of a sparse array according to one or more aspects of this disclosure is shown;

[0030] Figure 14 Exemplary tow cable sections according to one or more aspects of this disclosure are shown, including sensors; and

[0031] Figure 15 A system for processing data received from marine seismic tow cables, according to one or more aspects of this disclosure, is shown.

[0032] The same reference symbols in the various figures can indicate the same elements. Detailed Implementation

[0033] The following description relates to several embodiments and is intended to provide an understanding of those embodiments. This description is in no way intended to unduly limit the scope of any current or subsequent related claims.

[0034] Figure 1A An earthquake vessel 0 is shown towing a towline and a sound source across a body of water. The earthquake vessel 0 pulls at least one earthquake source 1 and at least one earthquake towline 2. The towline 2 is secured to the vessel 0 by an introduction cable 3, which is attached to a cable storage reel 4 located on the vessel. A stern buoy 5 is attached to the distal end of the cable by a long rope or similar material. The stern buoy may optionally be equipped with acoustic, electromagnetic, or visual devices for locating the end of the towline cable.

[0035] like Figure 1B As shown, each segment of the tow cable 2 contains multiple hydrophones 6, well-known in the field of seismology. The hydrophones are interconnected via transmission lines (not shown) to a remote recording device located on the ship. Adjacent hydrophones are connected by lines to form a group capable of generating a single output. Alternatively, each hydrophone is configured to generate a separate output g. i Then it is filtered in the process described below. Each segment of the tow cable may also include various sensors, such as those described below. Figure 11-13 The MEMS sensors discussed in the article.

[0036] Additionally, the towing cable includes a reinforcing member 7 designed to absorb tensile stresses applied to the cable during towing. The sensing and reinforcing components are surrounded by a plastic jacket 8 in the form of an elongated tube. The jacket is preferably filled with a light ballast fluid to make the section neutral or slightly positively buoyant. When filled with fluid, the interior of the jacket is essentially at atmospheric pressure. The cylindrical shape of the jacket is maintained by a plurality of baffles (not shown).

[0037] As the tow cable is dragged through the water, the air gun 1 is fired, and the resulting acoustic energy travels through the water column and the strata beneath the seabed. At various reflection points or planes, a portion of the acoustic energy is reflected. The cable of the hydrophone 6 receives the direct wave field as well as any reflected or refracted wave fields crossing the tow cable. In most cases, the received wave field is heavily contaminated by noise from various sources.

[0038] To attenuate unwanted noise in the received signal, the hydrophones 6 can be spaced 3.125 meters apart. Even though experimental data suggests that using a smaller sampling interval (e.g., 2.25 meters) can achieve better noise attenuation, the optimal spacing is still subject to several limitations, such as available bandwidth for data transmission and recording, or manufacturing costs. The values ​​mentioned above for hydrophone separation are derived from wet (kerosene-filled) towed cables; for other types of towed cables (e.g., solid and semi-solid towed cables), the sampling interval may need to be modified.

[0039] By combining the appropriate noise filtering methods described below, the selected sampling interval leads to a reduction in unwanted noise, particularly coherent noise such as bulge noise, expansion noise, and crossflow noise.

[0040] Now for reference Figure 2 The diagram shows an overall block diagram of an adaptive beamformer used as a filter to reduce noise recorded by a single sensor. Assume there are K sensors located at rk, where k = 1, ..., K. Each sensor k records a signal g using an A / D converter. k (n), where n = 1, ..., N. The letter "n" is used as the index of the discrete-time sample. The sampling interval is Δt. A delay τ is used. k Beam-directing the signal gk(n) towards the approximate "signal direction." This is the approximate direction from which the seismic signal is expected to arrive. The beam-directing channel x... k (n) is processed by a local multi-channel adaptive filter to produce the output signal:

[0041]

[0042] Where w ikv (t) are the adjustable coefficients of the adaptive filter, h i (n) is the window applied at the output, M is the number of local multi-channel adaptive filters (or the number of output windows), and L = L1 + L2 + 1 is the number of coefficients for each signal. Here and below, the hyphens under the letters indicate vectors (lowercase letters) or matrices (uppercase letters).

[0043] Click input vector at time t can be used x (n) Rewrite equation [1] as a (window form) sum over a scalar product:

[0044] x (n) ＝ [x1(n+L1),...,x1(n-L2)

[0045] x2(n+L1),...,x2(n-L2),

[0046] x k (n+L1),...,x k (n-L2)] T

[0047] Click weight vector w i Defined as

[0048]

[0049] Using definitions [2] and [3], equation [1] becomes

[0050]

[0051] Equations [1] and [4] describe the process once M click weighting vectors w are specified. i How to find the output of the beamformer or filter bank? Calculate these vectors as a solution to the optimization problem, as described below.

[0052] The optimization problem is defined as follows:

[0053]

[0054] Subject to the following constraints

[0055] C T w i = f

[0056] Where i = 1, 2, ..., M and J.

[0057]

[0058] and

[0059]

[0060] KL is the total number of filter coefficients, and ||.|| denotes the L2 norm. The cost function is a linear combination of the beamformer's output power (the first term in Equation [5]) and the beamformer's so-called "white noise gain" (the second term in Equation [5]), weighted by the input power. The relative weights of these two terms are determined by δ. 2 This adjustment, which includes the beamformer's "white noise gain" in the cost function, aims to improve the beamformer's robustness in the presence of signal modeling uncertainties (sometimes called perturbations) and numerical correlations between the signal and noise.

[0061] Equation [6] describes the Q-linear constraint on the acceptable solution of the optimization problem. Here, the KLxQ matrix... C It is a constraint matrix, Q vector f This is the response vector. The practical design of linear constraints is discussed below.

[0062] The optimal feasible solution depends on the window function h. i (n) Apply the following two constraints:

[0063]

[0064] For n = 1, 2, ..., N and

[0065] h i (n)h j (n)=0

[0066] For j<>i-1,i,i+1. The first constraint applies to all local filters (w). i The first constraint ensures that, under the same conditions, the filter bank is equivalent to a single filter. The second constraint ensures that the window has compact support.

[0067] The optimization problem can be largely decoupled by using the second condition (equation

[10] ) and the approximation

[11] .

[0068]

[0069] The approximation requirement of equation

[11] is that adjacent filters produce similar results when applied to the same input data in overlapping time regions of adjacent windows, rather than requiring adjacent filters to be similar point by point. Therefore, this approximation is similar to requiring the integrals of two functions to be close, rather than requiring the functions themselves to be close.

[0070] Through this approximation, the first term J1 of the cost function becomes

[0071]

[0072] in

[0073]

[0074] The second term in the cost function can be rewritten as:

[0075]

[0076] Where “tr” represents the trace of the matrix.

[0077] Combining equations (5), (12), and (14), and reorganizing each term, the total cost function can be written as:

[0078]

[0079] Where I represents the KL×KL identity matrix. The decoupling optimization problem can be solved for each of the M constrained time windows [6]. Using the Lagrange multiplier method, the optimal click weight for each window is...

[0080]

[0081] in

[0082]

[0083] The modified local correlation matrix can be The second term is considered as δ 2 The regularization term is used as a regularization parameter. In array signal processing literature, it has been suggested that in the case of narrowband beamforming, the correlation matrix be regularized by adding a scaled identity matrix to improve robustness in the presence of disturbances. Here, the cost function [5] includes the regularization term from the beginning, leading to the generalization of broadband adaptive beamforming. Therefore, the filter response varies with the signal frequency.

[0084] When the input data to the beamformer is characterized by spatially and temporally uncorrelated (or white) noise, the correlation matrix Φ i and the modified correlation matrix Proportional to the identity matrix. In this case, the optimal weight vector becomes

[0085]

[0086] Weight vector w q The static solution to the problem known as the optimal beamformer problem is called the static response. Note that the static solution depends entirely on the constraint matrix. C and response vector f .

[0087] With the regularization parameter δ 2 The increase in weight vector w, even for general noise fields, makes the optimal weight vector w... i It is also close to the static weight vector w q In this case, the modified correlation matrix It is close to the identity matrix (see

[17] ). Therefore, the regularization parameter δ 2 The optimal solution is weighted between solutions that depend entirely on the received data and solutions that are independent of the data. For δ 2 =1, meaning that the two solutions are equally weighted in terms of having equal trace values ​​in their corresponding correlation matrices. In cases of high perturbation, i.e., where the assumptions about seismic acquisition geometry do not hold entirely, finding a beamformer response with a higher level of regularization can provide more robust results. Another aspect of the invention relates to the design of linear constraints (equation [6]) imposed on the beamformer.

[0088] One type of linear constraint that can be applied to a beamformer is a linear constraint designed to preserve seismic signals incident from the target direction while suppressing interference from other directions. For example... Figure 2 The steering delay τ shown kA single "line of sight" is defined. Signals incident along this direction are in phase, and for these signals, the system can be considered as a single FIR (Finite Impulse Response) filter. The coefficient values ​​of this equivalent processor are equal to the sum of the corresponding coefficients in the adaptive processor. Each local beamformer w i Includes adaptive filters w that process data from each channel. i1 ,w i2 ,...,w ik And summation units. Each filter w i1 ,w i2 ,...,w ik The sum is constrained to give w eq This is the expected response of a signal incident along the line of sight (e.g., a unit pulse along the line of sight):

[0089]

[0090] For i = 1, ..., M, and w ik According to the following division

[0091]

[0092] The linear constraint equations [6] can be rewritten as matrix equations

[0093] C T w i = w eq = f ,

[0094] Where the KL×L matrix

[0095] C =[ I , I ,…, I ] T ,

[0096] It is a constraint matrix, and I It is an L×L identity matrix.

[0097] To produce a distortion-free response in the line-of-sight direction, you can choose... w eq As a unit pulse, for example

[0098] w eq =[0,0,...,0,1,0,...,0] T .

[0099] The static response then becomes the static response of a fixed-weight beamformer, where all elements have equal weights. In the frequency-wavenumber domain, this corresponds to a synchronization function that is constant in the f direction. Therefore, to increase the regularization parameter δ... 2 The value of the beamformer is such that it preserves signals incident not only from the line-of-sight direction but also from adjacent directions.

[0100] Now for reference Figure 3 This document provides a diagram depicting a marine seismic survey system 10 according to embodiments of the present disclosure. In the illustrated seismic survey system 10, a survey vessel 12 tows one or more multi-component seismic cables 14 (i.e., seismic tow cables) to its stern. The seismic tow cables 14 can be several kilometers long and can include various support cables as well as wiring and / or circuitry that can be used to support power and communication along the tow cables 14. Typically, each tow cable 14 includes a main cable in which seismic sensor units 16 for recording seismic signals are mounted. Seismic sensors can include hydrophones, seismographs, accelerometers, microelectromechanical systems (MEMS) sensors, or any other type of sensor that measures translational motion (e.g., displacement, velocity, and / or acceleration) of a surface, at least in the vertical direction and possibly in one or two horizontal directions. Such sensors are called translational survey sensors because they measure translational (or vector) motion. Each seismic sensor can be a single-component (1C), two-component (2C), or three-component (3C) sensor. A 1C sensor has one sensing element for sensing a wave field in a single direction; a 2C sensor has two sensing elements for sensing a wave field in two directions (which may be substantially orthogonal to each other, within design, manufacturing, and / or placement tolerances); a 3C sensor has three sensing elements for sensing a wave field in three directions (which may typically be orthogonal to each other). In the case of a multi-component seismic sensor, the sensor is capable of detecting at least one component of the pressure wave field and particle motion, which is associated with an acoustic signal near the multi-component seismic sensor. Examples of particle motion include one or more components of particle displacement, one or more components of particle velocity (linear (x), intersecting (y), and vertical (z) components (e.g., see axis 18)), and one or more components of particle acceleration.

[0101] Depending on specific embodiments of this disclosure, seismic sensors may include hydrophones, seismic detectors, particle displacement sensors, particle velocity sensors, accelerometers, pressure gradient sensors, or combinations thereof. For example, according to some embodiments of this disclosure, a particular multi-component seismic sensor arrangement may include a hydrophone for measuring pressure and three orthogonally aligned accelerometers to measure three corresponding orthogonal components of particle velocity and / or acceleration near the seismic sensor. Note that the multi-component seismic sensor assembly may be implemented as multiple devices that can be substantially located at the same site. A particular seismic sensor may include a pressure gradient sensor, which constitutes another type of particle motion sensor. Each pressure gradient sensor measures the change in the pressure wave field at a specific point relative to a specific direction. For example, one pressure gradient sensor may acquire seismic data indicating the partial derivative of the pressure wave field at a specific point with respect to the direction of intersection, while another pressure gradient sensor may acquire seismic data indicating pressure data at a specific point relative to the direction of approach.

[0102] The marine seismic survey (i.e., data acquisition) system 10 includes a seismic source 20, which may be formed by one or more seismic source elements (e.g., air guns) connected to the survey vessel 12. Alternatively, in other embodiments of this disclosure, the seismic source 20 may operate independently of the survey vessel 12, as the seismic source may be coupled to other vessels or buoys, as just a few examples.

[0103] As the seismic tow cable 14 is towed behind the survey vessel 12, the seismic source 20 generates an acoustic signal 22, commonly referred to as a "cannonball," and directs it downwards through the water column 24 into the strata 26 and 28 below the seabed surface 30. The acoustic signal 22 originates from various subsurface geological strata (e.g., Figure 3 The stratum 32 shown in the figure reflects light.

[0104] In some embodiments, the incident acoustic signal 22 generates a corresponding reflected acoustic signal or pressure wave 34, which is sensed by the seismic sensor unit 16. Note that the pressure waves received and sensed by the seismic sensor unit 16 include “upward” pressure waves that propagate to the sensor unit 16 without reflection, and “downward” pressure waves generated due to reflection from the pressure wave 34 at the air-water boundary 36.

[0105] In some embodiments, the seismic sensor unit 16 generates a signal (e.g., a digital signal) called a “trace” that indicates measurements of the acquired pressure wave field and particle motion (if the sensor is a particle motion sensor). According to some embodiments of this disclosure, the trace is recorded and can be at least partially processed by a signal processing unit 38 deployed on the survey vessel 12.

[0106] In some embodiments, the purpose of seismic acquisition is to create an image of the survey area for identifying subsurface geological strata 32. Subsequent analysis of the representation can reveal the possible locations of hydrocarbon deposits within the subsurface geological strata. Depending on a particular embodiment of this disclosure, portions of the analysis of the representation can be performed on the seismic survey vessel 12, such as via signal processing unit 38.

[0107] In some embodiments, the construction of a marine seismic cable may include a long tubular body. The body may include an outer skin that surrounds one or more reinforcing members, seismic sensors, spacers supporting the skin, filler material, and electrical wiring that transmits power and information between the various components (e.g., processors and sensors). Typically, the filler material has a density that maintains neutral buoyancy throughout the cable.

[0108] In marine seismic cables, the internal workings of the cable are supported in various ways. It should be understood that the internal support structure of the towed cable contributes to the sensor's measurement capabilities, as the sensors are highly sensitive and noise is a significant consideration. A structure might be sufficient to support the sensor and associated wiring, but introduce unacceptable noise levels into the readings. Conversely, a support structure that is acceptable in terms of noise and other signal detection may not provide adequate structural support. Furthermore, it is possible to properly support the sensor and provide appropriate noise properties, but the hardware cost might be too high to be commercially viable. The subtle details of the support structure of a seismic towed cable can have a significant impact on the performance of the sensors within the towed cable and the overall product cost.

[0109] Figure 4 A portion of a seismic tow cable 14 carrying a sensor unit 16 according to aspects of this disclosure is shown, the sensor unit being decoupled from and "floating" within the tow cable. The tow cable 14 includes an outer skin 40 defining an outer surface 42 and an inner surface 44, the outer skin being formed in a longitudinally extending tubular shape. The inner surface 44 of the outer skin 40 defines an internal volume 46. At least one reinforcing member 48 (e.g., KEVLAR, a registered trademark of DuPont) extends longitudinally through the internal volume 46, for example, in a direction parallel to the longitudinally extending tubular shape. Figure 4In this internal volume 46, a pair of spaced-apart reinforcing members 48 extend longitudinally. For example, the reinforcing members 48 may be spaced apart and positioned approximately 180 degrees apart from each other. A sensor unit 16 according to an aspect of this disclosure is disposed in the internal volume 46. The internal volume 46 is filled with a filler material 54 to support the sensor unit and the outer skin, as well as other components such as wires 56. The filler material 54 may be a gas, liquid, gel, or foam, which can provide sensing performance properties and support the internal hardware within the outer skin. The filler material (e.g., gel or foam) can be used to reduce (decouple) the accelerometer from the cable skin and / or reinforcing members. It should be noted that various gel or foam materials are well known and commercially available. In the depicted example, a spacer 58 is also arranged in the internal volume to support the outer skin. Non-limiting examples of spacer 58 are described, for example, in U.S. Patent Publications 2009 / 0323468, 2011 / 0273957 and 2018 / 0136348, the teachings of which are incorporated herein by reference.

[0110] In some embodiments, the depicted sensor unit 16 includes a sensor 50 (e.g., an accelerometer) and sensor electronics 49 disposed within and carried by a longitudinally extending sensor housing 52. The seismic sensor 50 may include at least one microelectromechanical system (MEMS)-based sensor accelerometer, which may be advantageous due to its size, low power consumption, and low cost. The sensor housing 52 includes a first end 51 and a second end 53 separated from each other in the longitudinal direction. According to one embodiment, the length of the sensor housing 52 is greater than about 100 mm. According to one embodiment, the sensor housing is greater than about 150 mm. According to one embodiment, the sensor housing extends about 200 mm or more in the longitudinal direction. When configured in this manner, the sensor may be a gradient sensor. The accelerometer may be a biaxial or triaxial accelerometer. The longitudinal sensor housing may be made of, for example, metal or polymer. The cross-section of the sensor housing 52 may be circular or non-circular. The longitudinal sensor housing 52 may have, for example, a flat outer surface 60 on which a buoy or buoyancy element 61 may be attached. For example, in Figure 4 In this configuration, the sensor unit 16, which includes the buoyancy element 61, can be in a substantially neutral buoyancy within the filler material 54. By placing the sensor unit 16 in a neutral buoyancy relative to the filler material (e.g., the sensor unit and a filler having the same density), the sensor 50 is coupled to the filler material 54. This may be desirable, for example, when the sensor is decoupled from a mechanical reinforcement member. In some embodiments, the sensor unit 16 may not include the buoyancy element 61. It should be recognized that the mounting configuration of the sensor 50, i.e., the sensor unit 16, can be selected in conjunction with the selection of the filler material 54, the outer skin 40 material, and the materials of the reinforcement member 48, as these components affect the noise characteristics.

[0111] Now for reference Figures 5 to 9 An embodiment of sensor unit 16 is shown, comprising a longitudinal sensor housing 52 arranged co-located with a sensor of spacer device 62, such that the sensor housing 52 extends through the center of spacer device 62 and extends from its opposite side. The sensor housing 52 can be arranged such that it extends substantially equal distances from the opposite sides of the spacer device (i.e., symmetrically). The sensor housing 52 can be an integral part of spacer device 62 or can be a separate, independent element. The sensor housing 52 can be acoustically coupled to the sensor spacer device 62 and the seismic cable, for example, see [reference needed]. Figure 6 and Figure 7 Alternatively, it can be acoustically decoupled from the sensor spacer device 62 and the seismic cable, for example, see [link to relevant documentation]. Figure 8 .

[0112] In some embodiments, the sensor spacer device 62 has a circular profile such that when positioned within the inner volume of the outer skin 40, the outer surface 64 (i.e., the outer radius) is substantially similar to the inner surface 44 (i.e., the inner radius) of the skin 40. In the example shown, the outer radius 64 of the sensor spacer device 62 has a generally designated 65 ( Figure 6 ), especially the parts specifically marked 65-1, 65-2, etc., which are radially separated from each other to contact an inner radius of 44 ( Figure 7 This allows the sensor spacer assembly to be supported within the skin 40. The opposing portions 65 are radially separated from each other, for example, within a range of approximately 120 to 180 degrees. For example, refer to... Figure 6 The outer radius portions 65-1 are separated from each other within a range of approximately 120 to 180 degrees, while the outer radius portions 65-2 are separated from each other within a range of approximately 120 to 180 degrees. The sensor spacer assembly 62 includes a longitudinally extending channel 66 or groove that opens along the outer radius 64 to the inner surface of the outer skin. The channel 66 defines a longitudinally extending passage through which (a plurality of) reinforcing members 48 and internal components such as wiring 56 can pass. The sensor spacer assembly 62 may have a sensor housing 52 integrated or mounted thereto, which extends from the opposite side of the sensor spacer assembly 62 and carries a seismic sensor 50, such as a MEMS accelerometer. The sensor housing 52 may, for example, be aligned with the central longitudinal axis 68 of the sensor spacer assembly 62. Figure 5 Extending coaxially. The sensor spacer device 62 is not limited to... Figure 5-9 The configuration shown.

[0113] In some embodiments, such as Figure 6-8As shown, the sensor housing 52 can be positioned through a central passage 70 that extends longitudinally along a longitudinal axis through the sensor spacer assembly 62. When the sensor housing and the spacer assembly are separate components and the sensor housing extends through the central passage or opening in the spacer assembly, the sensor housing can be of a generally non-circular shape to match the non-circular central passage 70, thus preventing rotation of the sensor housing within the central passage 70. Figure 6-8 In the example shown, the sensor spacer device 62 is formed as two segments 62-1 and 62-2, which are connected together at corresponding latching ends 63-1 and 63-2. In some embodiments, the spacer device is constructed as a single component, and in some embodiments, the spacer device may consist of more than two segments. The sensor spacer device is not limited to the configuration shown.

[0114] In some embodiments, it should be understood that, depending on the desired measurement, the MEMS sensor may be a 1C, 2C, or 3C sensor. The MEMS sensor may have axes that are perpendicular to each other or otherwise configured. One approach for directional accelerometers is to have its axis perpendicular to the surface of the sensor housing, with one axis aligned with the tow cable, while another axis is perpendicular to the tow cable and perpendicular to the surface.

[0115] Figure 6 and Figure 7 This is a longitudinal end view of an example of the sensing unit 16, wherein the sensor housing 52 and the carried sensor are coupled to the sensor spacer device 62. Figure 7 In this configuration, the sensor housing 52 and the sensor it carries are anchored to the mechanical frame of the tow cable 14, i.e., the reinforcing member 48, via a spacer device 62. The sensor housing 52 physically contacts and engages with the opposite section or side of the sensor support device 62, thereby rigidly connecting the sensor housing 52 and the accelerometer to the sensor support device. Figure 7 In the middle, two reinforcing members 48 extend through the interior of the tow cable 14 and through the channel 66 defined by the sensor spacer device 62. Figure 6 The connection between the sensor spacer assembly 62 and the reinforcing member 48 is tight, thereby anchoring the sensor spacer assembly to the reinforcing member, and... Figure 7 In this embodiment, sensor 50 is rigidly connected to the movement or vibration of the reinforcing member. This configuration also connects (couples) the movement of the tow cable skin 40 to sensor 50. Inside the tow cable 14, a filler material 54, such as gel, can surround the device, thus positively contributing to the support aspects of this design and its sensing performance. While gel can be used, it should be understood that other materials can be used.

[0116] Now for reference Figure 8The longitudinal end view of the tow cable 14 shows the sensing unit 16, in which the sensor housing 52 and the sensor 50 are located in the same position as the spacer device 62 and are decoupled from the spacer device and the seismic cable 14, for example, by a damping material such as decoupling foam 54. Different types of filler material 54 can be used in different sections of the tow cable. The sensor housing 52 extends through the central passage 70 of the spacer device 62, but does not make direct physical contact with the spacer device, but is located within the foam 54 arranged in the central passage 70. In the example shown, a buoyancy element 61 is attached to the sensor housing 52 to provide neutral buoyancy to the sensor housing 52. Using the buoyancy element 61 and / or selecting filler material to make the sensor unit neutrally buoyant, the sensor 50 is coupled to the surrounding filler material.

[0117] exist Figure 7 and Figure 8 In this configuration, sensor 50 can be substantially centered on the longitudinal axis of tow cable 14; however, sensor 50 can be positioned off-center. An off-center sensor 50 will be more susceptible to receiving some form of noise, and this noise can be filtered more easily by intentionally and more clearly recording it (e.g., noise shaping).

[0118] Figure 9 A portion of a seismic cable 14 incorporating a sensor unit 16 is shown according to an embodiment of this disclosure. See also... Figures 5 to 8 The sensor spacer device 62 is disposed within the internal volume 46 of the skin 40, with its outer radius 64 approaching or contacting the inner radius 44 of the skin. The longitudinal sensor housing 52 carrying the sensor 50 extends through the central passage 70 of the sensor support device 62. At least one and in Figure 8 In the sensor housing 52 and sensor 50, two spaced reinforcing members 48 extend through the longitudinal internal volume 46 of the outer skin 40 and through the channel 66 of the sensor spacer assembly 62. The sensor housing 52 and sensor 50 may be coupled or decoupled from the sensor support assembly 62 and the reinforcing members 48. The internal volume may include a filling material 54, such as a gas, liquid, gel, or foam.

[0119] It should be understood that different sensor unit configurations (e.g., decoupled and floating, decoupled and co-located with spacer devices, and coupled to co-located spacer devices) may be used within the same tow cable or even the same tow cable segment, depending on operational requirements. Although the various figures show individual sensor units in the tow cable, each tow cable segment may include two or more sensor units, which may be spaced evenly or unevenly along the cable.

[0120] It should be understood that noise is a problem in any seismic survey. Noise can be removed during data processing using various techniques, but it can also be controlled (e.g., shaped) by selecting a specific sensor mounting design. This can be illustrated by the fact that a single tow cable segment can actually have many (sometimes hundreds) individual sensors. A large number of sensors helps to provide data that can be processed more easily to eliminate noise. The large number of sensors required to filter noise negatively impacts the cost of the tow cable. Each additional sensor scattered throughout increases the cost of the system due to the cost of the sensor and its packaging, the cost of power and communication overhead (i.e., the cost of other components required to power the sensor and record its data), and the cost of processing the data from this additional sensor. If the sensors are isolated from noise, fewer sensors can be used, resulting in acceptable results. The design described in this paper helps to reduce noise levels (e.g., decouple) and shape sensed or received noise, making the noise characteristics easier to filter out in subsequent processing stages.

[0121] Now for reference Figure 10-13 This disclosure provides embodiments of a compression sensing marine towed cable system. It should be noted that any of the embodiments described below can be used in whole or in part in conjunction with some or all of the embodiments provided in Figures 1-9. More specifically, these embodiments relate to marine towed cable seismic exploration using a towed marine cable having one or more sensors (e.g., microelectromechanical system sensors (“MEMS”)) distributed at advantageous spacing.

[0122] For example, refer to again Figure 3-4 Each tow cable 14 may include a main cable in which a seismic sensor unit 16 for recording seismic signals is mounted. The seismic sensor may include a particle motion sensor, a hydrophone, a seismograph, an accelerometer, a microelectromechanical system (MEMS) sensor, or any other type of sensor that measures translational motion (e.g., displacement, velocity, and / or acceleration) of a surface, at least in the vertical direction and possibly in one or two horizontal directions. The specific arrangement and spacing of the sensors are discussed in further detail below.

[0123] The embodiments included herein can at least partially utilize single-sensor Q-Marine and multi-measurement IsoMetrix technologies (available from the assignee of this disclosure), while reducing costs by applying compressive sensing theory. By incorporating accelerometers and optimized gel rheology into a field-proven Q-Marine platform, the embodiments included herein deliver high-quality seismic data at low cost.

[0124] As described above, in some embodiments, compressed sensing theory techniques can be employed, which enable the generation of 3D deghosted data using fewer sensors, thereby reducing costs. To enable the layout to be used with standard processing workflows, the embodiments included herein can utilize a custom coherent signal and noise regression (CSNR) method to normalize and attenuate the noise in the data recorded by the non-uniformly sampled accelerometer.

[0125] In some embodiments, this disclosure may utilize, in whole or in part, a compression sensing system, some of which may include, but are not limited to, the IsoMetrix CS system from the assignee of this disclosure.

[0126] In some embodiments, the compression sensing techniques described herein can be built on existing platforms, and can also be introduced into gel platforms for efficient, low-cost design. By combining state-of-the-art accelerometer measurements with a robust and cost-effective solid gel platform, the novel compression sensing tow cable delivers the highest quality seismic data at low cost.

[0127] In some embodiments, and as discussed in further detail below, the compression sensing system included herein may utilize accelerometer technology, wherein particle motion is measured in three orthogonal directions to transmit acceleration along the Y and Z cable axes. Additionally and / or alternatively, as described above, this accelerometer technology may be coupled to a hydrophone. This can help transmit measurements of the pressure wave field and its derivatives to allow for accurate 3D receiver-side deghosting of the wave field and filling of the receiver ghost notch, thereby providing truly multi-measurement broadband data.

[0128] In some embodiments, and to achieve high data quality even in challenging drag environments, accelerometer configuration and gel rheology (e.g., the physical properties of the gel) can be core elements of the new platform design. According to the designs and embodiments of this disclosure, noise propagation characteristics can be shaped to reduce noise by utilizing single-sensor technology and using a gel with sufficient rheological properties.

[0129] For example, Figure 10 This illustrates how the gel transmits acceptable noise on a particle motion sensor. More specifically, this figure shows how the noise propagation characteristics of a towed platform are affected by gel rheology. The left-hand plot shows a level of noise attenuation at low frequencies, while the right-hand plot shows the noise energy up to high frequencies.

[0130] In some embodiments, high-quality particle motion measurements may be required to obtain the full benefits of a multi-sensor tow cable. This can be challenging because particle motion sensors are extremely sensitive to vibrations propagating through the tow cable. For example, towing a long tow cable under axial tension inevitably generates vibrations. These vibrations may have wavelengths much smaller than those of seismic signals and may travel long distances along the tow cable before decaying. The amplitude of the vibrations may be several orders of magnitude stronger than the signal of interest. Exemplary vibrations may typically include torsional vibrations that may be caused by the rotational motion of the cable over time, longitudinal vibrations that may be caused by compression and elongation of the tow cable, and lateral vibrations that may be caused by the dynamic bending of the tow cable. As will be discussed in more detail below, maximum wavenumbers (i.e., acoustic signals, torsional vibrations, longitudinal vibrations, and lateral vibrations) have been observed in the data received from multiple particle motion sensors, with the maximum wavenumber corresponding to the maximum wavenumber of the lateral vibration noise.

[0131] Classical Nyquist sampling theory dictates a uniform sensor distribution where at least two single-sensor measurements are performed for each shortest wavelength acquired, regardless of whether that wavelength is associated with a signal or noise. This uniform distribution is often referred to as the Nyquist spacing, meaning the maximum possible uniform spacing (distance between sensors) of sensors while ensuring aliasing-free measurements. In the aforementioned single-sensor tow cable, a uniform hydrophone spacing of no more than 3.125 meters ensures aliasing-free broadband pressure measurements across the entire wavefield, covering both signal and noise. As with analog groups, this facilitates subsequent digital preprocessing and noise attenuation of the raw measurements without requiring coarse spatial sampling.

[0132] In some embodiments, and also referring to Figures 11 to 14 The seismic towed cable system described in this paper utilizes a specially constructed 3-axis MEMS accelerometer to measure the particle acceleration of sound waves, which can substitute for spatial pressure gradients. This high-precision, low-noise, low-power, miniature accelerometer can achieve a stable, flat frequency response from DC to several kHz. It has a dynamic range of 130 dB, excellent vector fidelity, and can capture all information from low-amplitude cross-line pressure gradients reflected from beneath the surface to high-amplitude vibration noise from the cable. Furthermore, DC measurements can be converted to rotations of the gravity vector.

[0133] However, while the maximum uniform hydrophone spacing of 3.125 m captures the noise component of pressure measurements, slowly propagating vibration noise may require Nyquist spacing of tens of centimeters. An accelerometer sampling density ten times higher would make the tow cable extremely expensive and complex. Therefore, the embodiments included herein provide an accelerometer layout based on the principles of compression sensing theory, allowing for a significantly smaller number of accelerometers than required by classical Nyquist theory.

[0134] As used in this paper, the concept of compressed sensing is based on the fact that real-world measurements tend to have structure; they rarely have band-limited white noise with random phase, for which classic Nyquist sampling was designed. Instead, data recovery algorithms in compressed sensing assume that the structure in the data has a sparse representation. This is indeed the case with regard to cable vibration noise. For example, a cable may not simultaneously experience all possible outgoing vibration velocities around each sensor; instead, it will experience several distinct noise patterns locally.

[0135] Therefore, refer to again Figure 11-14 Hybrid strategies can be used to optimize non-uniform accelerometer layouts. Typically, the sensor spacing in the classical sampling theorem depends on the maximum wavenumber present in the data, i.e., the Nyquist wavenumber. As will be discussed in more detail below, the sampling interval can depend on the effective wavenumber width of the acoustic signal obtained through non-uniform sampling and the lateral vibration noise. As mentioned above, when the sensor spacing is restricted to uniformity, the number of sensors required to record aliasing-free noise can become excessive, which is therefore unreasonable. The simplest form of the Nyquist-Shannon sampling theorem requires the sampling rate to be greater than the Nyquist rate, i.e., twice the maximum wavenumber in the data. Thus, the sensor spacing used for uniform sampling cannot be greater than the reciprocal of the two-sided wavenumber width. In some implementations, the maximum wavenumber of the data can be the maximum wavenumber of the lateral vibration noise. As mentioned above, this is often referred to as the Nyquist spacing. From the perspective of the acoustic signal, for an acoustic signal propagating horizontally in the direction of approach, for a maximum frequency of, for example, 150 Hz and a minimum apparent velocity of, for example, 1500 m / s, the two-sided wavenumber width of the signal is 0.2 m. -1 This means that the sensor spacing should not exceed 5 meters during uniform sampling to record all information in the non-aliased signal cone. The sensor spacing may be larger if the acoustic signal is assumed to be sparse or if the slower apparent velocity portions of the acoustic signal are sacrificed. From a noise perspective, the sampling spacing should be selected based on the phase velocity of the slowest noise mode. Transverse noise has the slowest apparent velocity among transverse vibration noise, longitudinal vibration noise, and torsional vibration noise. In some embodiments, the two-sided wavenumber-width of transverse vibration noise may require, for example, a sensor spacing of 0.625 meters for solid marine seismic sensors and, for example, 0.3676 meters for gel-filled marine seismic sensors. In this way, even with some aliasing allowed, the number of sensors required for a 100-meter section of a gel-filled towed cable can be, for example, 272 sensors and / or, for example, 160 sensors for a 100-meter section of a solid marine seismic towed cable.

[0136] In some embodiments, a non-uniform layout may include spacing multiple MEMS sensors at least in part based on the effective wavenumber width of the acoustic signal and the lateral vibration noise. As described above, it has been observed that the maximum wavenumber in the data (i.e., acoustic signal, lateral vibration, torsional vibration, and longitudinal vibration) corresponds to the maximum wavenumber of the lateral vibration noise. In some embodiments, the effective wavenumber-width can be determined from the Gabor wavenumber-width. For example, using Fourier transform... The Gabor wavenumber-width W of a signal s(x) can be defined as the square root of the second moment of its spectrum normalized by the zeroth moment, as shown in Equation 24 below:

[0137]

[0138] The definition of the nth order moment is shown in Equation 25 below:

[0139]

[0140] In some embodiments, the zeroth moment may correspond to the average power, and the second moment may be a measure of spectral spread. The definition of Gabor wavenumber width is particularly applicable to single-component signals with low-pass spectra and located near zero wavenumber. For example, when the signal is multi-component and each component has a bandpass spectrum, the Gabor wavenumber width overestimates the actual spectral spread of the signal. In some embodiments, the effective wavenumber width K of a single-component signal, which is the Gabor wavenumber width, is... i,E Around its center of mass k i The calculation is shown in Equation 26:

[0141]

[0142] The integration range can cover the energy i of the signal component.

[0143] Essentially, it can be assumed that the spectra of different components occupy non-overlapping bands in the wavenumber. In some embodiments, the centroid k can be estimated from the data. i In some embodiments, the effective wavenumber-width of a multi-component signal can be defined as the sum of the effective wavenumber-widths of each component, as shown in Equation 27 below:

[0144]

[0145] In some embodiments, when the data consists of an acoustic signal and transverse vibration noise, the effective wavenumber-width can be the sum of the width of the acoustic signal (e.g., a signal cone) and the effective wavenumber-width of the transverse vibration, and the noise propagates in the +x and -x directions. In some embodiments, and for a wide frequency range, the estimated effective wavenumber-width of the transverse vibration noise can be approximately 0.03 m. -1Furthermore, when considering negative wavenumbers, the effective wavenumber-width of transverse vibration noise can be approximately 0.06m. -1 In some embodiments, the sampling interval may depend on the effective wavenumber width and lateral vibration noise of the acoustic signal, rather than on the two-sided wavenumber-width of the Nyquist-Shannon sampling.

[0146] In some embodiments, the sampling interval can be increased by depending on the effective wavenumber-width of the transverse vibration noise and the acoustic signal obtained through non-uniform sampling. For example, consider a Fourier transform... The signal s(x) is shown in Equation 28:

[0147]

[0148] In some embodiments, the Poisson summation equation can link the periodic summation of the signal s(x) to samples of its Fourier transform (k), as shown in Equation 29:

[0149]

[0150] Where c>0 is the period of the summation. In some embodiments, equation 29 can be valid regardless of the space and wavenumber of the signal s(x).

[0151] In some embodiments, it can be assumed that the signal s(x) has been spatially contracted so that its amplitude smoothly decreases to zero at the boundary of the observation interval [-c / 2, c / 2]. It can be assumed that most of the energy in the wavenumber domain is confined to the interval [-K / 2, K / 2], where K is the effective two-sided wavenumber-width. Thus, the infinite summation of Equation 29 becomes finite, and the Poisson summation equation can be simplified to Equation 30:

[0152]

[0153] Where the integer EEE is the space-wavenumber-width product. Although Equation 30 assumes an even EEE, the only modification for an odd EEE would be to change the summation range from -(P-1) / 2 to (P-1) / 2.

[0154] In some embodiments, equation 30 can define a continuous domain signal s(x) over the interval [-c / 2, c / 2]. Matrix notation can represent samples of the continuous domain signal on a discrete receiver array as x = [x1, K, x...]. M ] T As shown in equation 31:

[0155]

[0156] Where s can be a measured M-dimensional vector, F = P -1 / 2exp(j2πxk T ) is an M×P-dimensional Fourier matrix, and is a P-dimensional vector of Fourier coefficients.

[0157] In some embodiments, k can be set p = p / X, Fourier coefficients are calculated on a uniform wavenumber grid, and is a vector of wavenumbers. So far, it is only assumed that s is tapered in space, and the wavenumber approximation is limited to K / 2. It is now assumed that s is also sparse in terms of wavenumbers. In other words, some coefficients of the P-dimensional Fourier coefficient vector are actually zero. If the number of non-zero Fourier coefficients is N<P and the corresponding wavenumbers are represented, Equation 31 is equivalent to Equation 32:

[0158]

[0159] Since wavenumber coordinates can be equally spaced with Δk=1 / X, the effective wavenumber-width of a signal with N non-zero Fourier coefficients is K E = N / X. In some embodiments, the linear transformation defined by Equation 32 can map an N-dimensional vector of Fourier coefficients to a measured M-dimensional vector. If different Fourier coefficient vectors are mapped to different measurement vectors, the transformation is an injective or one-to-one transformation. In terms of notation, if then s₁(x)≠s₂(x). Equivalently, if s₁(x)=s₂(x), then an injective transformation is desirable because there exists an operation that can uniquely recover from a given s(x). After recovering , the Poisson summation equation shown in Equation 29 can be used to calculate the continuous-domain signal at any position in its domain [-X / 2, X / 2].

[0160] Conversely, a non-injective transformation can map multiple Fourier coefficient vectors to the same measurement. In terms of notation, may result in s₁(x)=s₂(x). In signal processing, this phenomenon is called aliasing. In other words, two different continuous-domain signals are indistinguishable when sampled on the receiver array x. Therefore, unless some other prior information can be obtained, the measurement alone is insufficient to recover the data.

[0161] A classic theorem in linear algebra states that the linear transformation of Equation 32 associated with the receiver array x and wavenumber support k′ is injective if and only if the columns of the sampled Fourier matrix F(x,k′) are linearly independent. A necessary condition for linear independence is that F(x,k′) has more rows than columns. Therefore, Equation 33 below shows the necessary condition for avoiding aliasing:

[0162] M≥N=XK E

[0163] Due to Δx av =X / M is the average receiver spacing of M receivers in the interval [-X / 2, X / 2]. Therefore, the necessary condition to avoid aliasing can also be written as shown in the following equation 34:

[0164] Δx ave ≤1 / K E

[0165] In some embodiments, the non-equation of Equation 34 can provide an upper limit on the average sensor spacing. Conversely, the sensor spacing requirement under uniform sampling constraints depends on the two-sided wavenumber-width, as shown in Equation 35:

[0166] Δx u ≤1 / (2K)

[0167] Combining equations 34 and 35, the average sensor spacing for aliasing-free sampling should satisfy 1 / (2K)≤Δx ave ≤1 / K E In the worst-case scenario, as specified by the Nyquist-Shannon interpolation theorem, the average sensor spacing is 1 / (2K) when the data is sparse. However, for lateral vibrations, an average sensor spacing close to 1 / K can be obtained. E (It is a non-aliased signal greater than 1 / (2K)). To obtain this benefit, it may be necessary to recover the continuous domain signal from its non-uniform samples.

[0168] In some embodiments, the input to the Coherent Signal and Noise Regression (CSNR) algorithm may include samples of data at known receiver locations, statistical information on unknowns, and spectral support for a coherent signal comprising acoustic and vibrational noise. A significant feature of the CSNR algorithm is the explicit use of a probabilistic prior for the amplitude vector, which is quite different from the spectral-based prior used in earlier trace interpolation algorithms. As will be discussed in more detail below and using a Bayesian estimation framework, a maximum a posteriori estimate of the amplitude vector can be derived given a set of basic vectors. For example, the choice of prior can lead to different interpolation methods, such as convex relaxation or regularized least squares regression in compressed sensing. Although the previously proposed spectral-based constraints reduce the number of interpolation parameters, the probability density prior stabilizes the interpolator by acting as an additional measurement. Consider the linear model shown in Equation 36 for data samples at known receiver locations:

[0169] d(t,x)=s(t,x)+w(t,x)

[0170] Where d(t,x) is the measurement value at time t and receiver position x, s(t,x) is the coherent signal, and w(t,x) is the accumulated noise.

[0171] In this model, the coherent signal s(t,x) consists of the acoustic signal and coherent vibration noise, while the incoherent noise n(t,x) represents calibration and modeling errors, disturbances, and any other broadband noise, as shown in the Fourier expansion of the coherent signal in Equation 37.

[0172]

[0173] Where integers It is the product of space-wavenumber-width, where X is space-width and K is the double-sided wavenumber-width. It is at frequency f and wavenumber k p The scaling Fourier transform coefficients when p / X = 0.

[0174] When from receiver array When a set of measurements is received, Fourier representation can be expressed in matrix form as shown in Equation 38:

[0175]

[0176] in The FX domain representation of the measured value is incoherent noise. It is the FK domain representation of the coherent signal, and the measurement kernel F = P -1 / 2 exp(j2πxk T ) is the Fourier inverse matrix, and It is a vector with uniformly spaced wavenumbers having the element p / X.

[0177] In some embodiments, since both the seismic signal and vibration noise have compact wavenumber support, only a subset of the corresponding Fourier coefficients are nonzero at any given frequency f:

[0178]

[0179] in It is a subset of the complete wavenumber vector k.

[0180] The reduced-dimensional vector k′ is a function of the signal cone, the vibration noise dispersion curve, and the wavenumber-width of the vibration noise at frequency f. However, for simplicity, frequency dependence is omitted. It can be assumed that the receiver array x has been designed as specified in the previous section, and therefore the matrix F(x,k′) has full column rank at all frequencies of interest.

[0181] The regression problem shown in Equation 39 corresponds to estimating the coefficients using the measured value d(x,f) and any other information about the acoustic signal, vibration noise, and incoherent noise w(x,f). Once these Fourier coefficient estimates are available at frequency f, the interpolation rule shown in Equation 40 can be used to interpolate any desired output grid at that frequency. The coherent portion of the calculated measurement values:

[0182]

[0183] The time-space domain representation of the signal can then be calculated using the inverse Fourier transform, as shown in Equation 41:

[0184] s est (y,t)=∫e j2πf s est (y,f)dk

[0185] As will be discussed in more detail below, statistical estimation techniques can be used to estimate the amplitude vector. For example, it can be assumed that at each frequency f, the accumulated noise w(x) and the amplitude vector It is a stochastic process W The implementation of (x), and ( The probability density functions are p w (w) and Frequency correlation of variables can be omitted to simplify notation. W (x) and They can be assumed to be independent of each other, and random processes at different frequencies can also be independent.

[0186] Incoherent noise can be modeled as a complex multivariate normal process with a joint probability density function, as shown in Equation 42 below:

[0187]

[0188] Where C W =E[ WW H ] is the complex covariance matrix, |C W | is the determinant of the covariance matrix. The mean of the multivariate normal distribution in Equation 42 is zero. It is said to be circularly symmetric because the random variable... W andee iα W For any They have the same distribution.

[0189] There are several options for the distribution of Fourier coefficients. For ease of discussion, the generalized normal distribution can be used because it offers flexibility in modeling different phenomena. Random variables with a generalized normal distribution... X The probability density function has the following form, as shown in Equation 43:

[0190]

[0191] in It is the complete gamma function, μ is the average value, and σ is the gamma function. 2 τ is the variance, and τ>0 is the shape parameter. Two important special cases of the generalized normal distribution can be obtained by setting τ=1, which gives the Laplace distribution; and τ=2, which gives the complex normal distribution.

[0192] We can further assume that the Fourier coefficients have a mean of zero and are independently distributed. Therefore, the joint probability density function of the Fourier coefficient vector is the product of the individual density functions, as shown in Equation 44:

[0193]

[0194] Where the covariance matrix It is a diagonal matrix.

[0195] In some embodiments, maximum likelihood estimation (MLE) finds a value for an unknown parameter as the value that maximizes its likelihood function. The likelihood function is closely related to the probability density function (PDF). Random variables X PDFp x (x; θ) is a function of the sampling point x, and is parameterized by the variable θ; likelihood function It is a function of the variable θ, and is a random variable. X The fixed implementation is calculated. In other words, for PDF p x (x; θ): x is a variable and θ is fixed; for the likelihood function θ is a variable, while x is fixed.

[0196] For the linear model shown in Equation 39, given the realization of the measurement vector d, the Fourier coefficient vector The likelihood function is

[0197]

[0198] The maximum likelihood estimation method discovers the parameter vector. The value of is used to maximize the likelihood function, as shown in Equation 46:

[0199]

[0200] The exponential function has a maximum value when it reaches its minimum. Therefore, the "ML" estimate is a method for solving this problem, as shown in Equation 47:

[0201]

[0202] Take the quadratic function relative to From the gradient, we obtain the normal equation:

[0203]

[0204] Alternatively, equation 48 can be solved using a fully orthogonal decomposition known in the art. This is achieved by applying a QR factorization with column pivots. Equation 49 is obtained.

[0205]

[0206] Where Q is an N×N orthogonal matrix, R is an N×M upper triangular matrix, and P is an M×M permutation matrix.

[0207] Then, by applying reduced QR factorization without pivoting R... H Equation 50 can be derived from this:

[0208] R H =Z1T1

[0209] Z1 is an M×N matrix with a single column, and T1 is an N×M upper triangular matrix.

[0210] In some embodiments, the matrix decomposition of Equation 51 can be a completely orthogonal decomposition.

[0211]

[0212] Using equation 52, it can be solved first by backward substitution. The following system of equations is used to calculate the ML solution, as shown in Equation 53:

[0213]

[0214]

[0215] Then multiply equation 53 by Q:

[0216]

[0217] In some embodiments, the maximum a posteriori (MAP) estimation method finds the values ​​of the unknown parameters as values ​​that maximize their posterior distribution. In Bayesian inference, the posterior distribution is the probability density function of the parameters to be estimated after observing the relevant quantities. For example, for the linear model shown in Equation 39, the distribution before any measurement is taken is... This is called the prior PDF, which obtains the distribution after measurement d. This is called a post-hoc PDF.

[0218] The posterior PDF can be computed using Bayes' theorem, which states that the posterior PDF is the prior PDF. and conditional PDF The product is obtained by measuring p. D (d) PDF normalization is shown in Equation 55 below:

[0219]

[0220] By using incoherent noise and the independence of Fourier coefficients, we can formulate a posterior PDF, as shown in Equation 56:

[0221]

[0222] Therefore, the Fourier coefficient vector The MAP estimate is the modulus of the posterior distribution equation 55. Since the denominator of equation 59 is a constant, the MAP estimate is the value that maximizes the numerator shown in equation 57:

[0223]

[0224] Substituting equations 42 and 46 into equation 57, we obtain the MAP estimate as a convex cost function as shown in equation 58. Minimum value:

[0225]

[0226] Equation 58 can be a equation with l τ The l2 cost function of the penalty term, where τ is the shape parameter of the generalized normal distribution. Special cases where the shape parameter τ is chosen as one or two are discussed below.

[0227] By choosing the shape parameter of the generalized normal distribution as τ = 1, the zero-mean Laplace distribution of equation 59 can be obtained.

[0228]

[0229] Therefore, the cost function used for MAP estimation becomes equation 60:

[0230]

[0231] Equation 60 can be a convex cost function, which appears in many problems such as sparse approximation, compressed sensing, and denoising. Although the nonsmoothness of the l1 norm prevents analytical solutions, many numerical methods exist to efficiently compute solutions. Some of these algorithms include gradient projection (GP), homotopy, iterative shrinkage thresholding (ITS), proximal gradient (PG), and enhanced Lagrange multiplier (ALM) methods. Alternatively, heuristic methods such as orthogonal matching pursuit (OMP) and minimum angular regression (LARS) provide approximate solutions.

[0232] Compared to the normal distribution, a prominent feature of the Laplace distribution is its heavy tails. The heavy tails of the distribution allow for vector... Some terms of the Laplace distribution occasionally exhibit large values, while others approach zero. This property of the Laplace distribution promotes sparse solutions.

[0233] While some applications search for sparse solutions, in others the sparsity of the solution is known beforehand. One such problem is interpolating an acoustic signal from a set of non-uniform receivers and coherent vibrational noise. In this case, we do not need to explicitly search for an N-sparse solution in a P-dimensional space where P >> N. This is because at each frequency f, we already know the signal cone of the acoustic signal, the dispersion wavenumber of the transverse vibration, and the effective wavenumber-width of the transverse noise, which determine which of the N Fourier coefficients is nonzero. For this case, there may be analytical solutions that can be efficiently implemented.

[0234] For example, by choosing the shape parameter of the generalized normal distribution as τ = 2, the multivariate complex normal distribution of equation 61 can be obtained:

[0235]

[0236] Substituting equations 42 and 61 into equation 58, we can prove that the posterior distribution is normal, and the mean is as shown in equation 62:

[0237]

[0238] Covariance:

[0239]

[0240] Since the magnitude of the normal distribution is the mean, the MAP estimator is the mean of the posterior distribution of equation 64:

[0241]

[0242] Woodbury's identity provides another expression for the MAP estimator, as shown in Equation 65:

[0243]

[0244] The matrix requiring the inverse is N-dimensional in Equation 64 and M-dimensional in Equation 65. Computationally, it is more advantageous to use Equation 64 when M > N and Equation 65 when the converse is true. Several recommended methods exist for calculating from Equation 64 or 65. Similar to ML estimation computations, a complete orthogonal decomposition can be used. Alternatively, Cholesky factorization, which has a slightly lower computational load, can be used.

[0245] Analyzing the constrained form of the MAP estimator provides useful information. If the prior covariance is zero, C... S If the value is 0, then the MAP estimator will become the prior mean (assumed to be zero in this discussion). This is equivalent to having a deterministic prior independent of the data. On the other hand, when prior information is insufficient, they have infinite covariance. In this case, the estimator is independent of the prior and is equivalent to an ML estimator, as shown in Equation 66:

[0246]

[0247] The choice of normal priors allows us to derive an analytical expression for the estimator's performance. The mean squared error (MSE) of the estimator can be defined as the variance of the estimation error, as shown in Equation 67:

[0248]

[0249] Where the estimator It is a random variable, and It is a truth value.

[0250] The well-known identity in estimation theory is that the mean square error is the sum of the variance of the estimator and the squared deviation of the estimator, as shown in Equation 68:

[0251] The variance is equivalent to the trace of the covariance matrix shown in Equation 69:

[0252]

[0253] Deviation is Expected value and true value The difference is shown in Equation 70:

[0254]

[0255] The first component of MSE is the variance (precision) of the estimator, while the second measures its bias (accuracy). To make the MSE small, the combined value of variance and bias should be small. For example, to calculate the MSE of MAP and ML estimators, the measurement model can be... Substitute into equations 64 and 66:

[0256]

[0257]

[0258] The expected value of the estimator may be:

[0259]

[0260]

[0261] The covariance matrix of the estimator can be:

[0262]

[0263]

[0264] Using equations 70 and 72, the bias between the MAP and ML estimators can be found, as shown in equation 74:

[0265]

[0266]

[0267] Therefore, the ML estimator has zero bias and is thus unbiased. On the other hand, the MAP estimator's bias depends on the true values ​​of the Fourier coefficients, and is therefore biased. In this way, the covariance matrix of the MAP estimator can be written from the covariance matrix of the ML estimator shown in Equation 75:

[0268]

[0269] This means that the variance of the MAP estimator is smaller than that of the ML estimator:

[0270]

[0271] Where expression C MAP <C ML Representing matrix C ML -C MAP It is positive.

[0272] Therefore, the ML estimator has a smaller bias; however, the MAP estimator has a smaller variance. While having an unbiased estimator may be tempting, Equation 68 shows that to obtain a smaller MSE, it may be necessary to make the combined value of the estimator variance and bias smaller. This brings the possibility that the estimator variance can be significantly reduced by allowing small biases in the estimator. This is especially true when the columns of the Fourier matrix F are almost collinear. In this case, because the matrix... It is almost singular, and the covariance matrix of the ML estimator given in Equation 73 is very large, so the ML estimator is unqualified. As mentioned above, this occurs in the presence of spatial aliasing or closely spaced receivers. On the other hand, the MAP estimator will always remain stable as long as the prior covariance matrix is ​​invertible.

[0273] By having a small estimator covariance, the MAP estimator can transmit a small mean squared error. The prior covariance controls the trade-off between bias and mean squared error. If the prior is too strong, the estimation will be too biased, while a very weak prior may not be sufficient to reduce the mean squared error. Therefore, the appropriate choice of prior is an important part of MAP estimation.

[0274] In some embodiments, a 100-meter segment of the marine seismic towed cable may include 56 MEMS sensors. Here, the optimized sparse sensor layout has an average spacing of at least 1.78 meters. In this particular example, 16 MEMS sensors have been placed on a uniform grid with a spacing of 6.25 meters, while the other 40 MEMS sensors have been pseudo-randomly placed. Thus, in some embodiments, at least two of the plurality of MEMS sensors may be placed adjacent to each other, with a spacing of 0.625 meters or less for solid towed cables and 0.39 meters or less for gel-filled towed cables. One or more adjacent MEMS sensors among the plurality of MEMS sensors may include an average spacing between 1 and 4 meters. For example, as described above, the average spacing may be approximately 1.78 meters (e.g., 100 meters / 56 sensors). In some embodiments, the average spacing may be approximately 3.125 meters (e.g., 100 meters / 32 sensors). In another example, the average spacing may be approximately 1.25 meters (e.g., 100 meters / 80 sensors). The marine seismic tow cable may further include an electronic core extending axially through an inner portion of the outer skin, wherein the plurality of sensors (e.g., particle motion sensors, MEMS sensors, etc.) are electrically communicated with the electronic core. It should be noted that the electronic core or system can be located along the seismic tow cable or at any suitable location within the seismic tow cable. The electronic core may include, but is not limited to, those discussed herein with reference to Figures 1-15. Although an example with 56 sensors has been discussed, it should be understood that any number of sensors can be used within the scope of this disclosure. For example, the number of sensors in such a sparse array arrangement discussed herein can range from approximately 32 to 100 sensors per 100 meters of tow cable. In a preferred embodiment, the number of sensors may include 56 to 80 sensors. In some embodiments, the number of sensors may range from approximately 56 to approximately 80 sensors.

[0275] As described above, in some embodiments, a marine seismic tow cable may include an outer skin formed in a longitudinally extending tubular shape, wherein the inner surface of the outer skin defines an internal volume containing, for example,... Figure 8 The filling material shown is a gel-like substance. The marine seismic towed cable may also include multiple hydrophones and multiple sensors associated with the outer skin, wherein, in the seismic towed cable, for every consecutive 100 meters of seismic towed cable, the multiple sensors include a predetermined minimum number of sensors (e.g., such as...). Figure 11-15 (As shown).

[0276] In some embodiments, the marine seismic tow cable may also include an electronic system extending through an internal portion of the seismic tow cable (e.g., axially and / or within the outer skin), wherein the plurality of sensors are electrically connected to the electronic system. Similarly, the electronic system may include any of the aspects discussed in Figures 1-15.

[0277] In some embodiments, the predetermined minimum number of sensors may include a subset of sensors having sensors that are more closely spaced than one or more of the remaining sensors in the plurality of sensors. The sensor subset may further include a first sensor attached to a first side of the outer skin and a second sensor attached to a second side of the outer skin. The plurality of sensors may include a three-component (“3C”) sensor. The marine seismic towline may include one or more seismic towline orientation detection devices configured to determine the relative position of at least a portion of the seismic towline.

[0278] In some embodiments, it can be assumed that the accelerometer noise has a sparse representation, while allowing the particle acceleration of the seismic signal to exist anywhere and everywhere within the so-called signal cone in the frequency-wavenumber domain. Therefore, signal components may indeed be oversampled, as the average accelerometer spacing may be shorter than the Nyquist-required spacing for all seismic signal wavelengths. Furthermore, the optimized non-uniform accelerometer layout can also be constrained to have a spacing along a set distance (e.g., as...). Figure 11 The sensors shown (each 6.25m) can actually be co-located with the hydrophone (the actual measurement of the system output).

[0279] refer to Figure 13 and 14 This provides a schematic diagram comparing conventional array and sparse array arrangements. Figure 13 The diagram illustrates a uniform Nyquist (all triangles) spacing and a non-periodic sparse (shaded triangles only) receiver layout. As shown, the sparse layout of shaded triangles can have 56 sensors. According to the conventional Nyquist spacing, all triangles (bright and shaded) overlap with a dense, uniform grid with a spacing of 6.25 / 17 meters, assuming some noise characteristics as an example. In other words, to follow the classical Nyquist sampling theorem to obtain unaliased signals and coherent noise, at least... Figure 13 Seismic sensors are placed at each of the triangular locations shown (light and dark). Similarly, Figure 14 A series of triangles (white and shaded) are shown above the line. Together, these triangles above the line illustrate the spacing required to meet the conventional Nyquist sampling interval, assuming various noise characteristics. However, this would result in 272 sensors per 100-meter segment of the marine seismic towed cable. Figure 14The sparse sensor configuration is also illustrated by bright-shaded triangles (above the line) and dark-shaded triangles (below the line) representing the sparse array arrangement. Figure 14 In the diagram, the dark-shaded triangles (below the line) show an irregular sparse layout. This sparse layout repeats every 12.5m along the length of the tow cable. The bright-shaded triangles (above the line) form an irregular sparse layout. This layout repeats every 100m or longer along the tow cable (i.e., the length of a tow cable segment). The layout can repeat over various lengths, but the length of the repeating pattern is likely always 12.5m or longer. For example, and in some embodiments, sensors (e.g., particle motion sensors, MEMS sensors, etc.) can be non-uniformly distributed along a continuous 100m length of the tow cable in a repeating pattern at intervals greater than 50m. It should be understood that... Figure 13-14 This is intended only to illustrate the axial spacing of the sensors along the tow cable, not the lateral or radial spacing. According to another embodiment, the number of sensors in the sparse array arrangement discussed herein can range from approximately 32 to 100 sensors per 100 meters of continuous tow cable length. In embodiments, the number of sensors can include 56 to 80 sensors. In some embodiments, the number of sensors can range from approximately 56 to approximately 80 sensors. It should be understood that... Figure 13-14 The illustration in the diagram is based on a uniformly spaced base grid. However, in practice, when defining the spacing of a sparse array, it is not necessary to base that spacing on a uniformly spaced base grid; for example, the sensor can be simply removed from a uniformly spaced base grid.

[0280] In some embodiments, sensors for a periodic layout cover the entire segment, while sensors for a non-periodic layout avoid the beginning and end of the segment. The fundamental principle behind this design choice for a non-periodic layout is at least in part based on prior knowledge of noise characteristics. For example, in a towed cable, the noise is strongest at the connector; silencing these sensors and interpolating the data generally provides higher data quality than attempting to eliminate noise from those sensors. Therefore, sensors can be distributed within the segment rather than placed in locations that might cause them to be silent.

[0281] Embodiments of this disclosure can be built upon established hydrophone technology while incorporating compressed sensing theory when designing accelerometer sensor layouts. In some embodiments, to enable the layout to be used with standard processing workflows, this disclosure may include a custom Coherent Signal and Noise Regression (CSNR) method to normalize and attenuate noise from data recorded by non-uniformly sampled accelerometers. CSNR is physics-based and signal-blind. It uses known physical properties of the cable to guide noise attenuation and makes no assumptions about the seismic signal; subsurface reflection gradients may exist anywhere and everywhere within the signal cone. This conservative approach is signal-safe while providing effective gradient noise attenuation for subsequent processing such as broadband 3D deghosting. CSNR outputs noise-attenuated accelerometer data at any desired uniform (embedded) grid. Embodiments of this disclosure can be used to facilitate cross-line wavefield reconstruction using the novel, optimized sparse accelerometer layouts included herein.

[0282] For example, and as mentioned above, non-uniform spacing of sensors can pose challenges to traditional, uniformly spaced sampling. The embodiments included herein can interpret seismic data from a set of non-uniformly spaced sensors as a statistical estimation problem. The input to a Coherent Signal and Noise Regression (CSNR) algorithm can be a sample of data at known receiver locations, statistical information about unknowns, and spectral support for a coherent signal including acoustic and vibration noise. This method can compute maximum likelihood and maximum a posteriori estimates of the Fourier coefficients, and then use linear regression to compute the signal and vibration noise at any desired location. This interpolation method is generally referred to as the Coherent Signal and Noise Regression (CSNR) algorithm, with a particular version implemented in the frequency and spatial domains as the FX-CSNR algorithm.

[0283] The embodiments included herein provide a method for performing seismic surveys. The method may include towing a marine seismic tow cable having an outer skin formed in a longitudinally extending tubular shape, the inner surface of which defines an internal volume containing a gel material. The method may further include acquiring seismic data using a plurality of hydrophones and a plurality of sensors associated with the outer skin, wherein, in the seismic tow cable, for every consecutive 100 meters of seismic tow cable, the plurality of sensors includes a predetermined minimum number of sensors. The method may further include transmitting the seismic data to an electronic system extending axially through the internal portion of the outer skin, wherein the plurality of sensors are electrically communicated with the electronic system.

[0284] Now for reference Figure 15 This paper provides an example of a data processing system associated with the marine seismic towed cable discussed in this paper. The volume of data and preprocessing requirements might necessitate extensive onboard hardware. The seismic towed cable described in this paper meets those requirements without requiring a large amount of onboard hardware and can be scaled up to operational needs.

[0285] In some embodiments, the recording system can be designed for high data volumes and speeds. Recording of single-sensor data allows for advanced preprocessing of the acquired data in near real-time, including identifying faulty sensors and rotating accelerometer sensors to their horizontal and vertical components. The recording system can deliver data in its original, continuously recorded format or a preprocessed, noise-attenuated format via recording tape from the Society for Exploration Geophysicists-D (SEG-D). Data can also be directly transmitted to any processing system via network-installed drop boxes.

[0286] In some embodiments, marine equipment can be controlled and monitored via a visual user interface with built-in alarms and equipment injection functionality. The entire instrumentation room can be controlled through a single configuration system. This ensures no data leaks and simplifies downstream processing. Network infrastructure, storage, processing servers, tape drives, and front-end display servers utilize standard, off-the-shelf components to improve reliability and reduce costs.

[0287] The block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of feasible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagram may represent a module, segment, or portion of code comprising one or more executable instructions for implementing the specified logical function(s). It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a non-consecutive order. For example, depending on the functions involved, two consecutively shown blocks may be executed substantially simultaneously, or sometimes in reverse order. It should also be noted that each block illustrated in the block diagram and / or flowchart, and combinations of blocks in the block diagram and / or flowchart illustration, may be implemented by a dedicated hardware-based system performing the specified function or action, or by a combination of dedicated hardware and computer instructions.

[0288] The foregoing has outlined features of several embodiments to enable those skilled in the art to better understand various aspects of this disclosure. Those skilled in the art will understand that they can readily use this disclosure as the basis for designing or modifying other processes and structures to achieve the same purposes and / or advantages as the embodiments described herein. Those skilled in the art should also recognize that such equivalent constructions do not depart from the spirit and scope of this disclosure, and that various changes, substitutions, and alterations can be made to them without departing from the spirit and scope of the invention. The scope of the invention should be determined solely by the language of the appended claims. The term “comprising” in the claims is intended to mean “at least comprising”, such that the list of elements enumerated in the claims is an open group. Unless expressly excluded, the terms “a,” “an,” and other singular terms are intended to include their plural forms.

[0289] The terminology used herein is for the purpose of describing particular example embodiments only and is not intended to limit this disclosure. It should also be understood that when the terms "comprising" and / or "including" are used in this specification, the presence of the stated feature, integer, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or combinations thereof is not excluded.

[0290] The equivalents of the corresponding structures, materials, actions, and devices or steps plus functional elements in the appended claims are intended to include any structure, material, or action used in conjunction with other claimed elements to perform a function. This disclosure has been given for purposes of illustration and description, but it is not intended to be exhaustive or to limit the disclosure to the forms disclosed. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of this disclosure. The embodiments were chosen and described in order to best explain the principles and practical application of this disclosure and to enable others skilled in the art to understand the various embodiments of this disclosure, which have various modifications suitable for the particular intended use.

[0291] Although some exemplary embodiments have been described in detail above, those skilled in the art will readily understand that many modifications are possible to the exemplary embodiments without substantially departing from the description of the marine seismic towline herein. Therefore, such modifications are intended to be included within the scope of this disclosure as defined by the appended claims. In the claims, the term "means plus function" is intended to cover not only structural equivalents but also equivalent structures, as described herein, of the structures performing the stated functions. Thus, although nails and screws may not be structural equivalents, since nails have a cylindrical surface for securing wooden parts together while screws have a helical surface, in the context of fastening wooden parts, nails and screws may be equivalent structures. The applicant's explicit intention is not to invoke any limitation of any claim herein from paragraph 6 of 35 U.S.SC §112, except where the claims expressly use "means for..." and the limitation of the associated function.

[0292] The disclosure of this application has thus been described in detail and with reference to its embodiments; it will be apparent that modifications and variations may be made without departing from the scope of this disclosure as defined in the appended claims.

Claims

1. A method for acquiring marine seismic data, comprising: A tow cable comprising multiple hydrophones and accelerometers is used, wherein the total number of accelerometers is less than the number required by the classical Nyquist sampling theorem for sampling the slowest noise pattern on the tow cable, and wherein a first set of accelerometers is uniformly spaced along the tow cable, a second set of accelerometers is non-uniformly spaced along the tow cable, and wherein data from the non-uniformly spaced accelerometers are processed using compression sensing theory.

2. The method according to claim 1, wherein, Processing data from non-uniformly spaced accelerometers using compressive sensing theory involves using coherent signals and noise regression to handle noise.

3. The method according to claim 1, wherein, Data from non-uniformly spaced accelerometers is processed using compressive sensing theory, including the processing of acoustic signals.

4. The method according to any one of claims 1 to 3, wherein, The evenly spaced accelerometers are actually co-located with the hydrophone.

5. The method according to any one of claims 1 to 3, wherein, The accelerometers are placed in a pattern that repeats at distances greater than 12.5 meters, with uneven spacing.

6. The method according to any one of claims 1 to 3, wherein, The accelerometers are placed in a non-repeating pattern at distances less than 100 meters.

7. The method according to any one of claims 1 to 3, wherein, The tow cable is a solid tow cable.

8. The method according to any one of claims 1 to 3, wherein, The tow cable is a gel-filled tow cable.

9. The method according to any one of claims 1 to 3, wherein, Hydrophone data and accelerometer data are used to perform ghosting.

10. The method according to any one of claims 1 to 3, wherein, Multiple towed cables were used for marine seismic data acquisition.

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